GB2368661A - Aspherical spectacle lens for correcting hereophoria of the eye - Google Patents

Abstract

An aspherical spectacle lens (1) has a prismatic power to correct hereophoria (visual axes being deviated during resting periods) of an eye. The spectacle lens has front (2) and back (3) surfaces, one of which is a rotationally-asymmetrical aspherical surface for correcting the aberrations caused by adding the prismatic power. When the back surface(3) is rotationally-asymmetrical, curvature of an intersection line (7) of a plane containing the normal (Z2) to the rotationally-asymmetrical surface at a framing reference point (4) and the rotationally-asymmetrical surface (3) at the prism base side may be larger than that at the apex side (i.e. in the area marked "R"). The framing reference point is coincident with a pupil position (5) of a user when the spectacle lens is installed on a frame. On the other hand, when the front surface (Fig 3, 12) is rotationally-asymmetrical, the curvature of the intersection line at the prism base side may be smaller than that at the apex side.

Description

236866 1

- 1 - Aspherical Spectacle Lens The present invention relates to a singlevision spectacle lens to correct eyesight and particularly, to an aspherical lens having a prismatic power to correct hereophoria of an eye.

15 A spectacle lens for correcting hereophoria (visual axes are deviated during a resting period) has a prismatic power.

A conventional aspherical lens produces the prismatic power by tilting a back surface (an eye side) with respect to a front surface (an object side).

20 Figs. 113 and 114 show an example of a conventional spectacle lens having a prismatic power) Fig. 113 is a sectional view and Fig. 114 is a plan view from the front surface. A spectacle lens 21 has a rotationallysymmetrical aspherical front surface 22 and a spherical back surface 23.

25 A framing reference point 24 is defined to be coincident with

- 2 - a pupil of an eye 5 of a user when the spectacle lens 21 is installed on a frame. In the drawings, a z:-axis is defined to be coincident with a normal to the front surface 22 at the frame reference point 24, and xl- and yl-axes, which intersect 5 at right angle, are defined in a plane that contacts with the front surface 22 and is perpendicular to the zl-axis. The Y1-

axis is direction from the base to the apex of the prism and the x -axis is perpendicular to both of the y:- and zl-axes in a left-hand coordinate system.

10 The front surface 22 does not tilt with respect to the x -y: plane, while the back surface 23 tilts with respect to the xl-yl plane. As a result, the spectacle lens 21 has a prismatic power whose base setting is the minus direction of the y:-axis.

15 However, since the above-described conventional spectacle lens is designed through the use of the front surface 22 and the back surface 23 that are originally designed for a lens having no prismatic power and it produces the prismatic power by tilting the front and back surfaces with respect to each 20 other, although it can correct hereophoria, aberration caused by adding the prismatic power is not taken into consideration.

It is therefore an object of the present invention to 25 provide an aspherical spectacle lens, which is capable of

- 3 having a sufficient optical performance even if the lens has a prismatic power to correct hereophoria of an eye.

According to an aspect of the present invention, aberration caused by adding a prismatic power is corrected by 5 a rotationally-asymmetrical surface. The aberration caused by adding the prismatic power is rotationally-asymmetrical and therefore, it is difficult to correct the aberration with a rotationally-symmetrical surface. According to an aspect of the present invention, one of front and back surfaces is 10 formed as a rotationally-asymmetrical aspherical surface, which can correct the aberration caused by adding the prismatic power.

In the case when the back surface is rotationally-

asymmetrical, it is preferable that curvature of an 15 intersection line of a plane containing the normal to the rotationally-asymmetrical surface at a framing reference point and the rotationally-asymmetrical surface at the prism base side is larger than that at the apex side. The framing reference point is coincident with a pupil position of a user 20 when the spectacle lens is installed on a frame, and is coincident with a prism reference point for a lens having a prismatic power. On the other hand, when the front surface is rotationally-asymmetrical, it is desirable that the curvature of the intersection line at the prism base side is 25 smaller than that at the apex side.

In more detail, the following condition (1) is preferably satisfied within the ranges of 10 h 20 and 30 < 0 150; C21(h, O+180)-C2 (h, 6) > 0.. .(1) where 5 C21(h, 0) = C2(h, 0) - C1(h, 0); Cl(h, O) is curvature of an intersection line of a plane, which contains a z1-axis and forms angle (degree) with respect to an xl-axis, and the front surface at a point whose distance from a zl-axis is h (mm); 10 C2(h, O) is curvature of an intersection line of a plane, which contains a z2-axis and forms angle a (degree) with respect to an x2-axis, and the back surface at a point whose distance from a z2-axis is h (mm); z -axis is a normal to the front surface at the framing 15 reference point; y1-axis is direction from the base to the apex in a plane perpendicular to the z1-axis; x1-axis is perpendicular to both of the Y1- and z -axes in a left-hand coordinate system; 20 z2-axis is a normal to the back surface at the framing reference point; y2-axis is direction from the base to the apex in a plane perpendicular to the z2-axis; and x2-axis is perpendicular to both of the Y2- and z2-axes 25 in a left-hand coordinate system.

- 5 - Further, it is preferable that the condition (2) is satisfied when the back surface is rotationally-asymmetrical and that the condition (3) is satisfied when the front surface is rotationally-asymmetrical; 5 C2(h, O+180)-C2(h, O) > 0 (2) C (h, O+180)-C (h, O) < 0 (3) Further, in order to respond to various combinations of spherical power, cylindrical power, cylindrical axis direction, prismatic power and base setting, it is desirable 10 that semifinished lens blanks whose front surfaces are finished are stockpiled and a back surface of the selected semifinished lens blank is processed according to the customer's specification in order to shorten delivery times.

Fig. 1 is a side sectional view of a spectacle lens embodying the invention whose back surface is rotationally asymmetrical; 20 Fig. 2 is a front view of the spectacle lens of Fig. 1; Fig. 3 is a side sectional view of a spectacle lens embodying the invention whose front surface is rotationally asymmetrical; Fig. 4 is a front view of the spectacle lens of Fig. 3; 25 Figs. 5A and 5B are tables showing distributions of

6 - curvature of the front and back surfaces, respectively, for the spectacle lens of a first embodiment; Fig. 6 is a graph showing variation of values of condition (1) with respect to variation of the angle 0 for the 5 spectacle lens of the first embodiment; Figs. 7A and 7B are graphs showing variations of curvatures of the front and back surfaces, respectively, with respect to variation of the distance h from the framing reference point for the spectacle lens of the first 10 embodiment; Figs. 8A and 8B are graphs showing variations of curvatures of the front and back surfaces, respectively, with respect to variation of the angle O for the spectacle lens of the first embodiment; 15 Figs. 9A and 9B are graphs showing variations of values of the conditions (3) and (2), respectively, with respect to variation of the angle for the spectacle lens of the first embodiment; Figs. lOA and lOB are three-dimension graphs showing an 20 average refractive power error and astigmatism, respectively, of the spectacle lens of the first embodiment; Figs. llA to 16B show data for the spectacle lens of a second embodiment in the same formats as Figs. 5A to lOB; Figs. 17A to 22B show data for the spectacle lens of a 25 first comparative example in the same formats as Figs. 5A to

- 7 - lOB; Figs. 23A to 28B show data for the spectacle lens of a third embodiment in the same formats as Figs. 5A to lOB; Figs. 29A to 34B show data for the spectacle lens of a 5 fourth embodiment in the same formats as Figs. 5A to lOB; Figs. 35A to 40B show data for the spectacle lens of a second comparative example in the same formats as Figs. 5A to lOB; Figs. 41A to 46B show data for the spectacle lens of a 10 fifth embodiment in the same formats as Figs. 5A to lOB; Figs. 47A to 52B show data for the spectacle lens of a sixth embodiment in the same formats as Figs. 5A to lOB; Figs. 53A to 58B show data for the spectacle lens of a third comparative example in the same formats as Figs. 5A to 15 lOB; Figs. 59A to 64B show data for the spectacle lens of a seventh embodiment in the same formats as Figs. 5A to lOB; Figs. 65A to 70B show data for the spectacle lens of a eighth embodiment in the same formats as Figs. 5A to lOB; 20 Figs. 71A to 76B show data for the spectacle lens of a fourth comparative example in the same formats as Figs. 5A to lOB; Figs. 77A to 82B show data for the spectacle lens of a ninth embodiment in the same formats as Figs. 5A to lOB; 25 Figs. 83A to 88B show data for the spectacle lens of a

- 8 - tenth embodiment in the same formats as Figs. 5A to lOB; Figs. 89A to 94B show data for the spectacle lens of a fifth comparative example in the same formats as Figs. 5A to lOBi 5Figs. 95A to lOOB show data for the spectacle lens of an eleventh embodiment in the same formats as Figs. 5A to lOB; Figs. lOlA to 106B show data for the spectacle lens of a twelfth embodiment in the same formats as Figs. 5A to lOB; Figs. 107A to 112B show data for the spectacle lens of 10 a sixth comparative example in the same formats as Figs. 5A to lOB; Fig. 113 is a side sectional view of a conventional spectacle lens; and Fig. 114 is a front view of the spectacle lens of Fig. 15 113.

An example of an aspherical spectacle lens embodying the 20 present invention will be described hereinafter. First, examples of general constructions of spectacle lenses embodying the invention will be described with reference to Figs. 1 to 4, and then concrete examples will be described.

Figs. 1 and 2 show a spectacle lens 1 whose front surface 25 2 is spherical and back surface 3 is rotationally

- 9 - asymmetrical; Fig. 1 is a sectional view and Fig. 2 is a plane view from the front surface 2. On the spectacle lens 1, a framing reference point 4 is defined to be coincident with a pupil of an eye 5 of a user when the lens 1 is installed on 5 a frame.

In the drawings, an x2-y2-z2 coordinate system whose origin is coincident with the framing reference point 4 is set for defining the back surface 3. The z2-axis is a normal to the back surface 3 at the framing reference point 4. The x2 10 and y2-axes intersect at right angle in a plane that is perpendicular to the z2-axis and contacts with the back surface 3 at the framing reference point 4. The y2-axis is a direction from the base to the apex of the prism, and the x2-

axis is perpendicular to both of the Y2- and z2-axes in a 15 left-hand coordinate system.

The back surface 3 does not tilt with respect to the x2-

Y2 plane, while the front surface 2 tilts with respect to the x2-y2 plane. Assuming that the x2-axis is coincident with the horizontal direction and the y2-axis is coincident with the 20 vertical axis under an as-worn condition, the spectacle lens 1 contains a prism whose base is located at down-side and apex is located at up-side, which is indicated as a "basedown" prismatic power.

The aspherical spectacle lens 1 corrects aberration 25 caused by adding the prismatic power by employing the

- 10 -

rotationally-asymmetrical shape of the back surface 3.

Namely, curvature of an intersection line 7 of a plane containing the normal to the back surface 3 at the framing reference point 4, which is the z2-axis, and the back surface 5 3 at the prism base side (the downside in the drawings) is larger than that at the apex side (the up-side). This setting corrects the aberration.

As shown in Fig. 2, a polar coordinate (h, O) and curvature C2(h, O) at the point (h, O) are defined. C2(h, 0) 10 is the curvature of the intersection line 7 of a plane, which contains a z2-axis and forms angle (degree) with respect to the x2-axis, and the back surface 3 at a point whose distance from the z2-axis is h (mm). The angle of the plus direction of the x2-axis equals 0 and it increases with the 15 counterclockwise rotation toward the apex side (the plus direction of the y2-axis).

The aspherical spectacle lens 1 satisfies the condition (2) within the range of 10 s h s 20 and 30 so s 150 that is indicated as an area R with a hatch pattern shown in Fig. 2; 20 C2(h, S+180)-C2(h, 0) > 0 (2) The value of C2(h, 0) is equal to a curvature at the point in the area R (the apex side) and the value of C2(h, 0+180) is equal to a curvature at the symmetric point (the base side) with respect to the origin. The condition (2) 25 represents that the curvature at the point in the area R is

- 11 -

smaller than the curvature at the symmetric point with respect to the origin. In the other words, it means that the curvature at the prism base side is larger than that at the apex side.

5 When the spectacle lens contains a cylindrical power to correct astigmatism of an eye, the addition cylindrical powers at a pair of symmetric points with respect to the origin are identical, which allows for satisfaction of the condition (2) irrespective of the cylindrical power.

10 For the spectacle lens 1 whose back surface 3 is rotationallyasymmetrical, the aberration caused by adding the prismatic power can be well corrected when the curvatures between the prism base side and the apex side are determined so as to satisfy the condition (2).

15 Figs. 3 and 4 show a spectacle lens 11 whose front surface 12 is rotationally-asymmetrical and back surface 13 is spherical; Fig. 3 is a sectional view and Fig. 4 is a plane view from the front surface 12. On the spectacle lens 11, a framing reference point 14 is defined to be coincident with 20 a pupil of an eye 5 of a user when the lens 11 is installed on a frame.

In the drawings, an x1-yl-zl coordinate system whose origin is coincident with the framing reference point 14 is set for defining the front surface 12. The z1-axis is a 25 normal to the front surface 12 at the framing reference point

- 12 14. The x1- and y:-axes intersect at right angle in a plane that is perpendicular to the z1-axis and contacts with the front surface 12 at the framing reference point 14. The y -

axis is a direction from the base to the apex of the prism, 5 and the x:axis is perpendicular to both of the Y1- and z1-axes in a left-hand coordinate system.

The front surface 12 does not tilt with respect to the x1-y plane, while the back surface 13 tilts with respect to the x1-yl plane. Assuming that the x -axis is coincident with 10 the horizontal direction and the y1axis is coincident with the vertical axis under an as-worn condition, the spectacle lens 11 contains a prism whose base is located at down-side and apex is located at up-side, which is indicated as a "base-

down" prismatic power.

15 The aspherical spectacle lens 11 corrects aberration caused by adding the prismatic power by employing the rotationally-asymmetrical shape of the front surface 12.

Namely, curvature of an intersection line 17 of a plane containing the normal to the front surface 12 at the framing 20 reference point 14, which is the z1-axis, and the front surface 12 at the prism base side (the down-side in the drawings) is smaller than that at the apex side (the up-side).

This setting corrects the aberration.

As shown in Fig. 4, a polar coordinate (h, O) and 25 curvature C1(h, O) at the point (h, 3) are defined. C (h, O)

- 13 is the curvature of the intersection line 17 of a plane, which contains a zl-axis and forms angle (degree) with respect to the x -axis, and the front surface 12 at a point whose distance from the zl-axis is h (mm). The angle of the plus 5 direction of the xl-axis equals 0 and it increases with the counterclockwise rotation toward the apex side (the plus direction of the yl-axis).

The aspherical spectacle lens 11 satisfies the condition (3) within the range of 10 s h s 20 and 30 so s 150 that is 10 indicated as an area R with a hatch pattern shown in Fig. 4; Cl(h, O+180) - Cl(h, 0) < 0...(3) The value of Cl(h, O) is equal to a curvature at the point in the area R (the apex side) and the value of Cl(h, 0+180) is equal to a curvature at the symmetric point (the 15 base side) with respect to the origin. The condition (3) represents that the curvature at the point in the area R is larger than the curvature at the symmetric point with respect to the origin. In the other words, it means that the curvature at the prism base side is smaller than that at the 20 apex side.

For the spectacle lens 11 whose front surface 12 is rotationallyasymmetrical, the aberration caused by adding the prismatic power can be well corrected when the curvatures between the prism base side and the apex side are determined 25 so as to satisfy the condition (3).

Further, the conditions (2) and (3) can be generalized to a condition (1). That is, the spectacle lenses 1 and 11 satisfy the following condition (1) within the range of 10 h 20 and 30 150i 5 C2 (h, S+180) - C2 (h, 9) > 0 (1) where C2l(h, O) = C2(h, O) - Cl(h, O).

The value of C2 (h, 9) is equal to a curvature difference at the point in the area R (the apex side) and the value of 10 Czl(h, O+180) is equal to a curvature difference at the symmetric point with respect to the origin (the base side).

The condition (1) represents that the curvature difference at the point in the area R is smaller than the curvature difference at the symmetric point with respect to the origin.

15 In other words, it means that the curvature difference at the prism base side is larger than that at the apex side.

The aberration caused by adding the prismatic power can be well corrected when the curvature differences between the prism base side and the apex side are determined so as to 20 satisfy the condition (1).

Next, twenty embodiments of the spectacle lens embodying the present invention will be described. In the following description, twelve embodiments and six comparative examples

will be described as compared with each other. In first, 25 third, fifth, sixth, seventh, eighth, ninth and eleventh

- 15 -

embodiments, a back surface has a rotationally-asymmetrical component to correct aberration caused by adding a prismatic power. In second, fourth, tenth and twelfth embodiments, a front surface has the rotationallyasymmetrical component for 5 the correction. Spectacle lenses of the comparative examples has a rotationally-symmetrical aspherical front surface and a spherical or a toric back surface. The lenses of the comparative examples produce the prismatic power by tilting the front surface with respect to the back surface in the same 10 manner as the conventional spectacle lens.

Further, two embodiments and one comparative example are designed for the same specification. For instance, the first

and second embodiments and the first comparative example are designed for the same specification, the third and fourth

15 embodiments and the second comparative example are designed for the same specification. Refractive index of lens material

equals 1.67 in all of the embodiments and the comparative examples.

20 First Embodiment The spectacle lenses of the first and second embodiments and the first comparative example are designed for satisfying the specification shown in TABLE 1. Each of these lenses has

a prismatic power to correct hereophoria while they do not 25 have a cylindrical power to correct astigmatism. In TABLE,

- 16 SPH denotes a vertex spherical power, CYL denotes a cylindrical power, AX denotes a direction of the cylinder axis, PRS denotes a prismatic power and BASE denotes a base setting of the prism. Unit of the prismatic power is (Prism 5 Diopter).

TABLE 1

SPH -4.00 Diopter CYL 0.00 Diopter 10 AX PRS 3.00

BASE 270 Base Down The aspherical spectacle lens of the first embodiment 15 satisfies the specification of TABLE 1, the front surface is

a spherical surface that has a uniform curvature 1.35 Diopter as shown in Fig. 5A, and the back surface is a rotationally-

asymmetrical aspherical surface whose curvature at the framing reference point is distributed among 7.35 to 7.36 Diopter as 20 shown in Fig. 5B. The tables in Figs. 5A and 5B show distributions of the curvatures C:(h, 6) and C2(h, O) of the front and back surfaces in the direction of the intersection line at the polar coordinate (h, O) where h is a distance (mm) from the origin and is an angle with respect to the x-axis 25 or x2axis. The center thickness of the lens of the first embodiment is 1.10mm.

Fig. 6 is a graph showing variation of C2 (h, O+180)-C2

- 17 l(h, O) that is left side of the condition (1) with respect to variation of the angle for the distances h = 10, 15, 20 and 25 mm In order to correct the aberration caused by adding the prismatic power, the values of the left side of the 5 condition (1) rise to maximums at = 90 and are reduced to minimums at = 270 for all of the distances h = 10, 15, 20 and 25 mm. The amplitude of the variation increases as the distance h becomes larger. Fig. 6 shows that the values indicated in the graph are larger than zero in the range of 10 30 150 for all of the distances h = 10, 15, 20 and 25 mm. Namely, the aspherical spectacle lens of the first embodiment satisfies the condition (1).

Figs. 7A and 7B are graphs showing variations of curvatures C:(h, O) and C2(h, 6) of the front and back 15 surfaces, respectively, with respect to variation of the distance h from the framing reference point for the angle 9 = 0 , 9 = 45 , = 90 , = 135 , = 180 , = 225 , = 270

and = 315 . Since the front surface is spherical, the curvature C (h, O) does not vary according to variations of 20 the distance h and the angle 6, the graph of Fig. 7A shows the straight lines overlapped to each other. Since the back surface is rotationally-asymmetrical, the curvature C2(h, O) varies according to variations of the distance h and the angle 3. In the graph of Fig. 7B, the curve of = 90 , the 25 overlapped curves of 6 = 45 and 135 , the overlapped curves

- 18 of 0 = 0 and 180 , the overlapped curves of 0 = 225 and 315 and the curve of 0 = 270 are arranged in increasing order of curvature, that is, from the left side in the graph.

Figs. 8A and 8B are graphs showing variations of 5 curvatures C (h, O) and C2(h, 0) of the front and back surfaces, respectively, with respect to variation of the angle O for the distances h = 10, 15, 20 and 25 mm. Since the front surface is spherical, the curvature C1(h, O) does not vary according to variations of the distance h and the angle 0, the 10 graph of Fig. 8A shows the straight lines overlapped to each other. In order to correct the aberration caused by adding the base-down prismatic power, the curvatures C2(h, 0) of the back surface are reduced to minimums at 0 = 90 and rise to maximums at 0 = 270 for all of the distances h = 10, 15, 20 15 and 25 mm as shown in Fig. 8B. The longer the distance h is, the smaller the curvature C2(h, 0) is.

Further, Figs. 9A and 9B are graphs showing variations of C1(h, O+180)C1(h, O) that is the left side of the condition (3) and C2(h, O+180)-C2(h, O) that is the left side 20 of the condition (2), respectively, with respect to variation of the angle O for the distances h = 10, 15, 20 and 25 mm.

Since the front surface is spherical, the value of the left side of the condition (3) remains constant. The value of the left side of the condition (2) varies according to variations 25 of the angle a and the distance h. For example, the point at

- 19 = 90 on the curve of h = lOmm represents the value C2(10, 270) C2(10, 90). In view of Fig. 5B, C2(10, 270) = 7.02 and C2(10,90) = 6.61, then C2(10, 270) - C2(10, 90) = 0.41. Fig. 9B shows that the values indicated in the graph are larger 5 than zero in the range of 30 a 150 for all of the distances h = 10, 15, 20 and 25 mm. Namely, the aspherical spectacle lens of the first embodiment satisfies the condition (2). Figs. lOA and lOB are three-dimension graphs showing 10 transmitting optical performances of the aspherical spectacle lens of the first embodiment; Fig. lOA shows an average refractive power error and Fig. lOB shows astigmatism. In the graphs, plane coordinates represent the angle of visual axis (unit: degree) in the vertical and horizontal directions, 15 respectively, and the vertical axis represents amount of aberration (unit: Diopter).

Second Embodiment . In the same manner as the first embodiment, the 20 aspherical spectacle lens of the second embodiment satisfies the specification of TABLE 1, the front surface is a

rotationally-asymmetrical aspherical surface whose curvature at the framing reference point is distributed among 2.44 to 2.45 Diopter as shown in Fig. llA, and the back surface is a 25 spherical surface that has a uniform curvature 8.46 Diopter

- 20 as shown in Fig. llB. The center thickness of the lens of the second embodiment is 1.10mm.

Fig. 12 is a graph showing variation of C21(h, O+180)-C2 1(h, 0) that is left side of the condition (1) with respect to 5 variation of the angle 0. In order to correct the aberration caused by adding the prismatic power, the values of the left side of the condition (1) rise to maximums at 0 = 90 and are reduced to minimums at = 270 for all of the distances h = 10, 15, 20 and 25 mm. The amplitude of the variation 10 increases as the distance h becomes larger. Fig. 12 shows that the values indicated in the graph are larger than zero in the range of 30 < 150 for all of the distances h = 10, 15, 20 and 25 mm. Namely, the aspherical spectacle lens of the second embodiment satisfies the condition (1).

15 Figs. 13A and 13B are graphs showing variations of curvatures C1(h, O) and C2(h, O) of the front and back surfaces, respectively, with respect to variation of the distance h from the framing reference point. Since the front surface is rotationally-asymmetrical, the curvature Cl(h, O) 20 varies according to variations of the distance h and the angle O. In the graph of Fig. 13A, the curve of = 270 , the overlapped curves of = 225 and 315 , the overlapped curves of 0 = 0 and 180 , the overlapped curves of = 45 and 135 and the curve of 0 = 90 are arranged in increasing order of 25 curvature. Since the back surface is spherical, the curvature

- 21 does not vary according to variations of the distance h and the angle 0, the graph of Fig. 13B shows the straight lines overlapped to each other.

Figs. 14A and 14B are graphs showing variations of 5 curvatures Cl(h, O) and C2(h, O) of the front and back surfaces, respectively, with respect to variation of the angle 9. In order to correct the aberration caused by adding the base-down prismatic power, the curvatures C1(h, O) of the front surface rise to maximums at 0 = 90 and are reduced to 10 minimums at 0 = 270 for all of the distances h = 10, 15, 20 and 25 mm as shown in Fig. 14A. The longer the distance h is, the larger the curvature Cl(h, 5) is. Since the back surface is spherical, the curvature C2(h, 0) does not vary according to variations of the distance h and the angle 8, the graph of 15 Fig. 14B shows the straight lines overlapped to each other.

Further, Figs. 15A and 15B are graphs showing variations of Cl(h, O+180)Cl(h, O) that is the left side of the condition (3) and C2(h, O+180)-C2(h, 9) that is the left side of the condition (2), respectively, with respect to variation 20 of the angle 0. The values of the left side of the condition (3) vary according to variations of the angle 3 and the distance h. Fig. 15A shows that the values indicated in the graph are smaller than zero in the range of 30 150 for all of the distances h = 10, 15, 20 and 25 mm. Namely, the 25 aspherical spectacle lens of the second embodiment satisfies

- 22 the condition (3). Since the back surface is spherical, the values of the left side of the condition (2) remain constant.

Figs. 16A and 16B are three-dimension graphs showing transmitting optical performances of the aspherical spectacle 5 lens of the second embodiment; Fig. 16A shows an average refractive power error and Fig. 16B shows astigmatism.

First Comparative Example In the same manner as the first and second embodiments, 10 the aspherical spectacle lens of the first comparative example satisfies the specification of TABLE 1, the front surface is

a rotationally-symmetrical aspherical surface whose curvature at the framing reference point is 2.44 Diopter as shown in Fig. 17A, and the back surface is a spherical surface that has 15 a uniform curvature 8.46 Diopter as shown in Fig. 17B. The center thickness of the lens of thefirst comparative example is l.lOmm.

Fig. 18 is a graph showing variation of C21(h, 3+180)-C2 (h, O) that is left side of the condition (1) with respect to 20 variation of the angle O. Since the front and back surfaces are rotationally-symmetrical, the value of the left side of the condition (1) remains constant. Namely, the aspherical spectacle lens of the first comparative example does not satisfy the condition (1).

25 Figs. l9A and l9B are graphs showing variations of

- 23 curvatures C (h, O) and C2(h, O) of the front and back surfaces, respectively, with respect to variation of the distance h from the framing reference point. Since the front surface is a rotationally- symmetrical aspherical surface, the 5 curvature varies according to variation of the distance h while the variation of the angle O does not change the curvature. In the graph of Fig. 19A, the curves of all of the angles are overlapped. Since the back surface is spherical, the curvature does not vary according to variations of the 10 distance h and the angle 0, the graph of Fig. l9B shows the straight lines overlapped to each other.

Figs. 20A and 20B are graphs showing variations of curvatures C (h, O) and C2(h, 9) of the front and back surfaces, respectively, with respect to variation of the angle 15 O. Since the front surface is a rotationallysymmetrical aspherical surface, the curvatures C:(h, O) are different in response to the distance h and do not vary according to variation of the angle e, the curvatures are shown as independent straight lines. Since the back surface is 20 spherical, the curvature C2(h, O) does not vary according to variations of the distance h and the angle 0, the graph of Fig. 20B shows the straight lines overlapped to each other.

Further, Figs. 21A and 21B are graphs showing variations of C1(h, 9+180)C:(h, O) that is the left side of the 25 condition (3) and C2(h, O+180)C2(h, O) that is the left side

- 24 of the condition (2), respectively, with respect to variation of the angle O. Since the front surface is a rotationally-

symmetrical aspherical surface, the value of the left side of the condition (3) remains constant. Further, since the back 5 surface is spherical, the value of the left side of the condition (2) remains constant. Namely, the spectacle lens of the first comparative example does not satisfy the conditions (2) and (3).

Figs. 22A and 22B are three-dimension graphs showing 10 transmitting optical performances of the aspherical spectacle lens of the first comparative example; Fig. 22A shows an average refractive power error and Fig. 22B shows astigmatism.

As compared with the graphs of the first and second embodiments (Figs. lOA, lOB, 16A and 16B) designed for the 15 same specification, a number of contour lines in either graph

of the first comparative example is larger than that of the embodiments, which shows that the optical performance of the embodiments is better than the comparative example. That is, when the rotationally-asymmetrical component is introduced 20 into the back surface or the front surface as in the first and second embodiment, the aberration is more sufficiently corrected as compared with the spectacle lens that merely tilts the front surface with respect to the back surface for adding a prismatic power as in the first comparative example.

- 25 Third Embodiment The spectacle lenses of the third and fourth embodiments and the second comparative example are designed for satisfying the specification shown in TABLE 2. Each of these lenses has

5 a prismatic power to correct hereophoria and a cylindrical power to correct astigmatism TABLE 2

SPH -4.00 Diopter 10 CYL -4.00 Diopter AX Do PRS 3.00

BASE _ 270 Base Down 15 The aspherical spectacle lens of the third embodiment satisfies the specification of TABLE 2, the front surface is

a spherical surface that has a uniform curvature 1.35 Diopter as shown in Fig. 23A, and the back surface is a rotationally asymmetrical aspherical surface whose curvature at the framing 20 reference point is distributed among 7.36 to 13.36 Diopter as shown in Fig. 23B. The center thickness of the lens of the third embodiment is 1.10mm. The back surface contains a first rotationally-asymmetrical component to correct the aberration caused by adding a prismatic power and a second rotationally 25 asymmetrical component to add a cylindrical power. Therefore, any rotationally-asymmetrical component is not required for the front surface, which allows the front surface to be formed

as a spherical surface.

Fig. 24 is a graph showing variation of C2l(h, O+180)-C2 (h, O) that is left side of the condition (1) with respect to variation of the angle O. In order to correct the aberration 5 caused by adding the prismatic power, the values of the left side of the condition (1) rise to maximums at = 90 and are reduced to minimums at = 270 for all of the distances h = 10, 15, 20 and 25 mm. The amplitude of the variation increases as the distance h becomes larger. Fig. 24 shows 10 that the values indicated in the graph are larger than zero in the range of 30 150 for all of the distances h = 10, 15, 20 and 25 mm. Namely, the aspherical spectacle lens of the third embodiment satisfies the condition (1).

Figs. 25A and 25B are graphs showing variations of 15 curvatures C (h, O) and C2(h, 0) of the front and back surfaces, respectively, with respect to variation of the distance h from the framing reference point. Since the front surface is spherical, the curvature C (h, O) does not vary according to variations of the distance h and the angle 9, the 20 graph of Fig. 25A shows the straight lines overlapped to each other. Since the back surface is rotationally-asymmetrical, the curvature C2(h, 0) varies according to variations of the distance h and the angle O. In the graph of Fig. 25B, the overlapped curves of = 0 and 180 , the overlapped curves of 25 = 45 and 135 , the overlapped curves of = 225 and 315 ,

- 27 the curve of 0 = 90 and the curve of = 270 are arranged in increasing order of curvature.

Figs. 26A and 26B are graphs showing variations of curvatures C1(h, O) and C2(h, O) of the front and back 5 surfaces, respectively, with respect to variation of the angle for the distances h = 10, 15, 20 and 25 mm. Since the front surface is spherical, the curvature C (h, O) does not vary according to variations of the distance h and the angle 6, the graph of Fig. 26A shows the straight lines overlapped to each 10 other. The curvature of the back surface becomes small at 3 = 0 and 180 and becomes large at = 90 and 270 due to the added cylindrical power, in general. However, the curvature at the side of the prism base (3 = 270 ) is larger than that at the side of the apex (O = 90 ) in order to correct the 15 aberration caused by adding the base-down prismatic power.

Further, Figs. 27A and 27B are graphs showing variations of C (h, O+180)C (h, O) that is the left side of the condition (3) and C2(h, O+180)-C2(h, O) that is the left side of the condition (2), respectively, with respect to variation 20 of the angle 9. Since the front surface is spherical, the value of the left side of the condition (3) remains constant.

The value of the left side of the condition (2) varies according to variations of the angle and the distance h. Fig. 27B shows that the values indicated in the graph are 25 larger than zero in the range of 30 0 150 for all of the

distances h = 10, 15, 20 and 25 mm. Namely, the aspherical spectacle lens of the third embodiment satisfies the condition (2). Figs. 28A and 28B are three-dimension graphs showing 5 transmitting optical performances of the aspherical spectacle lens of the third embodiment; Fig. 28A shows an average refractive power error and Fig. 28B shows astigmatism.

Fourth Embodiment 10 In the same manner as the third embodiment, the aspherical spectacle lens of the fourth embodiment satisfies the specification of TABLE 2, the front surface is a

rotationally-asymmetrical aspherical surface whose curvature at the framing reference point is distributed among 2.44 to 15 2.46 Diopter as shown in Fig. 29A, and the back surface is a toric surface whose curvature is distributed among 8.46 to 14.47 Diopter as shown in Fig. 29B. The center thickness of the lens of the fourth embodiment is 1.10mm.

Fig. 30 is a graph showing variation of C2 (h, 0+180)-C2 20:(h, 0) that is left side of the condition (1) with respect to variation of the angle O. In order to correct the aberration caused by adding the prismatic power, the values of the left side of the condition (1) rise to maximums at = 90 and are reduced to minimums at = 270 for all of the distances h = 25 10, 15, 20 and 25 mm. The amplitude of the variation

- 29 -

increases as the distance h becomes larger. Fig. 30 shows that the values indicated in the graph are larger than zero in the range of 30 9 150 for all of the distances h = 10, 15, 20 and 25 mm. Namely, the aspherical spectacle lens of 5 the fourth embodiment satisfies the condition (1).

Figs. 31A and 31B are graphs showing variations of curvatures C1(h, O) and C2(h, 0) of the front and back surfaces, respectively, with respect to variation of the distance h from the framing reference point. Since the front 10 surface is rotationally-asymmetrical, the curvature C:(h, O) varies according to variations of the distance h and the angle 6. In the graph of Fig. 31A, the curve of 0 = 270 , the overlapped curves of 9 = 225 and 315 , the curve of 0 = 90 , the overlapped curves of 9 = 0 and 180 and the overlapped 15 curves of 0 = 45 and 135 are arranged in increasing order of curvature. Since the back surface is toric, the curvature varies according to variation of the angle 0. However, the curvature of the toric surface does not vary according to variation of the distance h. Therefore, in the graph of Fig. 20 SIB, the overlapped straight lines of 0 = 0 and 180 , the overlapped straight lines of 0 = 45 , 135 , 225 and 315 , the overlapped straight lines of 0 = 90 and 270 are arranged in increasing order of the curvature.

Figs. 32A and 32B are graphs showing variations of 25 curvatures C1(h, O) and C2(h, O) of the front and back

- 30 surfaces, respectively, with respect to variation of the angle O. For the rotationally-asymmetrical front surface, the curvature C (h, O) at the side of the prism base (O = 270 ) is smaller than that at the side of the apex (O = 90 ) for all of 5 the distances h = 10, 15, 20 and 25 mm as shown in Fig. 32A in order to correct the aberration caused by adding the base-

down prismatic power. The curvature C2(h, O) of the boric back surface rises to a maximum at = 90 and 270 and is reduced to a minimum at = 0 and 180 .

10 Further, Figs. 33A and 33B are graphs showing variations of C:(h, 0+ 180)-C (h, O) that is the left side of the condition (3) and C2(h, 0+180)C2(h, O) that is the left side of the condition (2), respectively, with respect to variation of the angle O. The values of the left side of the condition 15 (3) vary according to variations of the angle and the distance h. Fig. 33A shows that the values indicated in the graph are smaller than zero in the range of 30 150 for all of the distances h = 10, 15, 20 and 25 mm. Namely, the aspherical spectacle lens of the fourth embodiment satisfies 20 the condition (3). Since the back surface is toric, the values of the left side of the condition (2) remain constant.

Figs. 34A and 34B are three-dimension graphs showing transmitting optical performances of the aspherical spectacle lens of the fourth embodiment; Fig. 34A shows an average 25 refractive power error and Fig. 34B shows astigmatism.

- 31 Second Comparative Example In the same manner as the third and fourth embodiments, the aspherical spectacle lens of the second comparative example satisfies the specification of TABLE 2, the front

5 surface is a rotationally-symmetrical aspherical surface whose curvature at the framing reference point is 2 44 Diopter as shown in Fig. 35A, and the back surface is a toric surface whose curvature is distributed among 8.46 to 14.47 Diopter as shown in Fig. 35B. The center thickness of the lens of the 10 second comparative example is 1.10mm.

Fig. 36 is a graph showing variation of C2l(h, O -180)-C2 (h, O) that is left side of the condition (1) with respect to variation of the angle 9. Since the front surface is rotationally-symmetrical and the back surface is symmetric 15 with respect to the framing reference point, the value of the left side of the condition (1) remains constant. Namely, the aspherical spectacle lens of the second comparative example does not satisfy the condition (1).

Figs. 37A and 37B are graphs showing variations of 20 curvatures C:(h, O) and C2(h, O) of the front and back surfaces, respectively, with respect to variation of the distance h from the framing reference point. Since the front surface is a rotationally-symmetrical aspherical surface, the curvature varies according to variation of the distance h 25 while the variation of the angle 9 does not change the

curvature. In the graph of Fig. 37A, the curves of all of the angles are overlapped. Since the back surface is toric, the curvature varies according to variation of the angle 0.

However, the curvature of the toric surface does not vary 5 according to variation of the distance h. Therefore, in the graph of Fig. 37B, the overlapped straight lines of = 0 and 180 , the overlapped straight lines of = 45 , 135 , 225 and 315 , the overlapped straight lines of 9 = 90 and 270 are arranged in increasing order of the curvature.

10 Figs. 38A and 38B are graphs showing variations of curvatures C1(h, 0) and C2(h, 0) of the front and back surfaces, respectively, with respect to variation of the angle 9. Since the front surface is a rotationallysymmetrical aspherical surface, the curvatures C1(h, O) are different in 15 response to the distance h and do not vary according to variation of the angle 0, the curvatures are shown as independent straight lines. The curvature C2(h, O) of the toric back surface rises to a maximum at 0 = 90 and 270 and is reduced to a minimum at = 0 and 180 .

20 Further, Figs. 39A and 39B are graphs showing variations of C:(h, 0+ 180)-C (h, O) that is the left side of the condition (3) and C2(h, O+180)C2(h, O) that is the left side of the condition (2), respectively, with respect to variation of the angle O. Since the front surface is a rotationally 25 symmetrical aspherical surface, the value of the left side of

- 33 the condition (3) remains constant. Further, since the back surface is toric, the value of the left side of the condition (2) remains constant. Namely, the spectacle lens of the second comparative example does not satisfy the conditions (2) 5 and (3).

Figs. 40A and 40B are three-dimension graphs showing transmitting optical performances of the aspherical spectacle lens of the second comparative example; Fig. 4OA shows an average refractive power error and Fig. 40B shows astigmatism.

10 As compared with the graphs of the third and fourth embodiments (Figs. 28A, 28B, 34A and 34B) designed for the same specification, a number of contour lines in either graph

of the second comparative example is larger than that of the embodiments, which shows that the optical performance of the 15 embodiments is better than the comparative example.

Fifth Embodiment The spectacle lenses of the fifth and sixth embodiments and the third comparative example are designed for satisfying 20 the specification shown in TABLE 3. Each of these lenses has

a prismatic power to correct hereophoria while they do not have a cylindrical power to correct astigmatism.

TABLE 3

SPH CYL 0.00 Diopter AX _ _ 5 PRS 3.00

BASE Z D' Base Down The aspherical spectacle lens of the fifth embodiment satisfies the specification of TABLE 3, the front surface is

10 a spherical surface that has a uniform curvature 0.68 Diopter as shown in Fig. 41A, and the back surface is a rotationally-

asymmetrical aspherical surface whose curvature at the framing reference point is distributed among 12.69 to 12.71 Diopter as shown in Fig. 41B. The center thickness of the lens of the 15 fifth embodiment is 1.10mm.

Fig. 42 is a graph showing variation of Couth, O+180)-C2 Ah, O) that is left side of the condition (1) with respect to variation of the angle O. In order to correct the aberration caused by adding the prismatic power, the values of the left 20 side of the condition (1) rise to maximums at = 90 and are reduced to minimums at = 270 for all of the distances h = 10, 15, 20 and 25 mm. The amplitude of the variation increases as the distance h becomes larger. Fig. 42 shows that the values indicated in the graph are larger than zero 25 in the range of 30 150 for all of the distances h = 10, 15, 20 and 25 mm. Namely, the aspherical spectacle lens of the fifth embodiment satisfies the condition (1).

- 35 Figs. 43A and 43B are graphs showing variations of curvatures C1(h, O) and C2(h, 0) of the front and back surfaces, respectively, with respect to variation of the distance h from the framing reference point. Since the front 5 surface is spherical, the curvature C (h, O) does not vary according to variations of the distance h and the angle 0, the graph of Fig. 43A shows the straight lines overlapped to each other. Since the back surface is rotationally-asymmetrical, the curvature C2(h, 0) varies according to variations of the 10 distance h and the angle a. In the graph of Fig. 43B, the curve of = 90 , the overlapped curves of = 45 and 135 , the overlapped curves of 0 = 0 and 180 , the overlapped curves of = 225 and 315 and the curve of = 270 are arranged in increasing order of curvature.

15 Figs. 44A and 44B are graphs showing variations of curvatures C (h, O) and C2(h, 3) of the front and back surfaces, respectively, with respect to variation of the angle 0. Since the front surface is spherical, the curvature Cl(h, a) does not vary according to variations of the distance h and 20 the angle a, the graph of Fig. 44A shows the straight lines overlapped to each other. In order to correct the aberration caused by adding the base-down prismatic power, the curvatures C2(h, 0) of the back surface are reduced to minimums at a = 90 and rise to maximums at = 270 for all of the distances 25 h = 10, 15, 20 and 25 mm as shown in Fig. 44B. The longer the

- 36 distance h is, the smaller the curvature C2(h, O) is.

Further, Figs. 45A and 45B are graphs showing variations of C:(h, O+180)C (h, O) that is the left side of the condition (3) and C2(h, O+180)-C2(h, O) that is the left side 5 of the condition (2), respectively, with respect to variation of the angle O. Since the front surface is spherical, the value of the left side of the condition (3) remains constant.

The value of the left side of the condition (2) varies according to variations of the angle 9 and the distance h. 10 Fig. 45B shows that the values indicated in the graph are larger than zero in the range of 30 < < 150 for all of the distances h = 10, 15, 20 and 25 mm. Namely, the aspherical spectacle lens of the fifth embodiment satisfies the condition (2). 15 Figs. 46A and 46B are three-dimension graphs showing transmitting optical performances of the aspherical spectacle lens of the fifth embodiment) Fig. 46A shows an average refractive power error and Fig. 46B shows astigmatism.

20 Sixth Embodiment In the same manner as the fifth embodiment, the aspherical spectacle lens of the sixth embodiment satisfies the specification of TABLE 3, the front surface is a

rotationally-symmetrical aspherical surface whose curvature 25 at the framing reference point is 1.73 Diopter as shown in

- 37 Fig. 47A, and the back surface is a rotationally-asymmetrical aspherical surface whose curvature at the framing reference point is distributed among 13.74 to 13.76 Diopter as shown in Fig. 47B. The center thickness of the lens of the sixth 5 embodiment is 1.10mm.

Fig. 48 is a graph showing variation of C2l(h, 0+180)-C2 (h, O) that is left side of the condition (1) with respect to variation of the angle 0. In order to correct the aberration caused by adding the prismatic power, the values of the left 10 side of the condition (1) rise to maximums at = 90 and are reduced to minimums at 0 = 270 for the distances h = 10, 15 and 20 mm. Fig. 48 shows that the values indicated in the graph are larger than zero in the range of 30 s 0 s 150 and 10 s h 20. Namely, the aspherical spectacle lens of the 15 sixth embodiment satisfies the condition (1).

Figs. 49A and 49B are graphs showing variations of curvatures Cl(h, 9) and C2(h, 0) of the front and back surfaces, respectively, with respect to variation of the distance h from the framing reference point. Since the front 20 surface is a rotationally-symmetrical aspherical surface, the curvature varies according to variation of the distance h while the variation of the angle O does not change the curvature. In the graph of Fig. 49A, the curves of all of the angles are overlapped. Since the back surface is 25 rotationally-asymmetrical, the curvature C2(h, O) varies

- 38 according to variations of the distance h and the angle O. In the graph of Fig. 49B, the curve of = 90 , the overlapped curves of = 45 and 135 , the overlapped curves of = 0 and 180 , the overlapped curves of = 225 and 315 and the 5 curve of = 270 are arranged in increasing order of curvature. Figs. 50A and 50B are graphs showing variations of curvatures C (h, O) and C2(h, O) of the front and back surfaces, respectively, with respect to variation of the angle 10 O. Since the front surface is a rotationally-symmetrical aspherical surface, the curvatures C:(h, 9) are different in response to the distance h and do not vary according to variation of the angle 8, the curvatures are shown as independent straight lines. In order to correct the 15 aberration caused by adding the base-down prismatic power, the curvatures C2(h, O) of the back surface rise to maximums at = 90 and are reduced to minimums at = 270 for the distances h = 10, 15 and 20 mm as shown in Fig. SOB. The longer the distance h is, the smaller the curvature C2(h, O) 20 is.

Further, Figs. 51A and 51B are graphs showing variations of C (h, O+180)C (h, O) that is the left side of the condition (3) and C2(h, 9+180)-C2(h, O) that is the left side of the condition (2), respectively, with respect to variation 25 of the angle O. Since the front surface is rotationally

- 39 symmetrical, the value of the left side of the condition (3) remains constant. The value of the left side of the condition (2) varies according to variations of the angle and the distance h. Fig. 51B shows that the values indicated in the 5 graph are larger than zero in the range of 30 9 150 and 10 h 20. Namely, the aspherical spectacle lens of the sixth embodiment satisfies the condition (2).

Figs. 52A and 52B are three-dimension graphs showing transmitting optical performances of the aspherical spectacle 10 lens of the sixth embodiment; Fig. 52A shows an average refractive power error and Fig. 52B shows astigmatism.

Third Comparative Example In the same manner as the fifth and sixth embodiments, 15 the aspherical spectacle lens of the third comparative example satisfies the specification of TABLE 3, the front surface is

a rotationally-symmetrical aspherical surface whose curvature at the framing reference point is 1.73 Diopter as shown in Fig. 53A, and the back surface is a spherical surface that has 20 a uniform curvature 13.76 Diopter as shown in Fig. 53B. The center thickness of the lens of the third comparative example is l.lOmm.

Fig. 54 is a graph showing variation of C2l(h, O+180)-C2 1(h, O) that is left side of the condition (1) with respect to 25 variation of the angle O. Since the front and back surfaces

- 40 are rotationally-symmetrical, the value of the left side of the condition (1) remains constant. Namely, the aspherical spectacle lens of the third comparative example does not satisfy the condition (1).

5 Figs. 55A and 55B are graphs showing variations of curvatures C1(h, 0) and C2(h, O) of the front and back surfaces, respectively, with respect to variation of the distance h from the framing reference point. Since the front surface is a rotationally-symmetrical aspherical surface, the 10 curvature varies according to variation of the distance h while the variation of the angle 3 does not change the curvature. In the graph of Fig. 55A, the curves of all of the angles are overlapped. Since the back surface is spherical, the curvature does not vary according to variations of the 15 distance h and the angle 8, the graph of Fig. 55B shows the straight lines overlapped to each other.

Figs. 56A and 5GB are graphs showing variations of curvatures C1(h, O) and C2(h, O) of the front and back surfaces, respectively, with respect to variation of the angle 20 O. Since the front surface is a rotationallysymmetrical aspherical surface, the curvatures C (h, O) are different in response to the distance h and do not vary according to variation of the angle 0, the curvatures are shown as independent straight lines. Since the back surface is 25 spherical, the curvature C2(h, O) does not vary according to

- 41 variations of the distance h and the angle 0, the graph of Fig. 56B shows the straight lines overlapped to each other.

Further, Figs. 57A and 57B are graphs showing variations of Cl(h, O+180)Cl(h, e) that is the left side of the 5 condition (3) and C2(h, O+180)C2(h, O) that is the left side of the condition (2), respectively, with respect to variation of the angle 3. Since the front surface is a rotationally-

symmetrical aspherical surface, the value of the left side of the condition (3) remains constant. Further, since the back 10 surface is spherical, the value of the left side of the condition (2) remains constant. Namely, the spectacle lens of the third comparative example does not satisfy the conditions (2) and (3).

Figs. 58A and 58B are three-dimension graphs showing 15 transmitting optical performances of the aspherical spectacle lens of the third comparative example; Fig. 58A shows an average refractive power error and Fig. 58B shows astigmatism.

As compared with the graphs of the fifth and sixth embodiments (Figs. 46A, 46B, 52A and 52B) designed for the same 20 specification, a number of contour lines in either graph of

the third comparative example is larger than that of the embodiments, which shows that the optical performance of the embodiments is better than the comparative example.

25 Seventh Embodiment

- 42 The spectacle lenses of the seventh and eighth embodiments and the fourth comparative example are designed for satisfying the specification shown in TABLE 4. Each of

these lenses has a prismatic power to correct hereophoria and 5 a cylindrical power to correct astigmatism.

TABLE 4

SPH -8.00 Diopter CYL -4.00 Diopter 10 AX 9oo PRS 3.00

BASE 270 Base Down The aspherical spectacle lens of the seventh embodiment 15 satisfies the specification of TABLE 4, the front surface is

a spherical surface that has a uniform curvature 0.68 Diopter as shown in Fig. 59A, and the back surface is a rotationally-

asymmetrical aspherical surface whose curvature at the framing reference point is distributed among 12.69 to 18.72 Diopter 20 as shown in Fig. 59B. The center thickness of the lens of the seventh embodiment is 1.10mm. The back surface contains a first rotationally-asymmetrical component to correct the aberration caused by adding a prismatic power and a second rotationally-asymmetrical component to add a cylindrical 25 power. Therefore, any rotationally-asymmetrical component is not required for the front surface, which allows the front surface to be formed as a spherical surface.

- 43 Fig. 60 is a graph showing variation of C21(h, 0+180)-C2 1(h, O) that is left side of the condition (1) with respect to variation of the angle 6. In order to correct the aberration caused by adding the prismatic power, the values of the left 5 side of the condition (1) rise to maximumsat 0 = 90 and are reduced to minimums at 0 = 270 for the distances h = 10, 15 and 20. The amplitude of the variation increases as the distance h becomes larger. Fig. 60 shows that the values indicated in the graph are larger than zero in the range of 10 30 s 150 for all of the distances h = 10, 15, 20 and 25 mm. Namely, the aspherical spectacle lens of the seventh embodiment satisfies the condition (1).

Figs. 61A and 61B are graphs showing variations of curvatures C1(h, 0) and C2(h, 0) of the front and back 15 surfaces, respectively, with respect to variation Of the distance h from the framing reference point. Since the front surface is spherical, the curvature C:(h, O) does not vary according to variations of the distance h and the angle 0, the graph of Fig. 61A shows the straight lines overlapped to each 20 other. Since the back surface is rotationally-asymmetrical, the curvature C2(h, O) varies according to variations of the distance h and the angle 0. In the graph of Fig. 61B, the curve of 0 = 90 , the curve of = 270 , the overlapped curves of = 45 and 135 , the overlapped curves of = 225 and 25 315 , the overlapped curves of = 0 and 180 are arranged in

- 44 increasing order of curvature.

Figs. 62A and 62B are graphs showing variations of curvatures Cl(h, O) and C (h,2 0) of the front and back surfaces, respectively, with respect to variation of the angle 5 O. Since the front surface is spherical, the curvature C,(h, 9) does not vary according to variations of the distance h and the angle 0, the graph of Fig. 62A shows the straight lines overlapped to each other. The curvature of the back surface becomes large at = 0 and 180 and becomes small at = 90 10 and 270 due to the added cylindrical power, in general.

However, the curvature at the side of the prism base (O = 270 ) is larger than that at the side of the apex (S = 90 ) in order to correct the aberration caused by adding the base-down prismatic power.

15 Further, Figs. 63A and 63B are graphs showing variations of C (h, 3+ 180)-C (h, O) that is the left side of the condition (3) and C2(h, 0+180)C2(h, 9) that is the left side of the condition (2), respectively, with respect to variation of the angle O. Since the front surface is spherical, the 20 value of the left side of the condition (3) remains constant.

The value of the left side of the condition (2) varies according to variations of the angle and the distance h. Fig. 63B shows that the values indicated in the graph are larger than zero in the range of 30 < 150 for all of the 25 distances h = 10, 15, 20 and 25 mm. Namely, the aspherical

- 45 spectacle lens of the seventh embodiment satisfies the condition (2).

Figs. 64A and 64B are three-dimension graphs showing transmitting optical performances of the aspherical spectacle 5 lens of the seventh embodiment; Fig. 64A shows an average refractive power error and Fig. 64B shows astigmatism.

Eighth Embodiment In the same manner as the seventh embodiment, the 10 aspherical spectacle lens of the eighth embodiment satisfies the specification of TABLE 4, the front surface is a

rotationally-symmetrical aspherical surface whose curvature at the framing reference point is 1.01 Diopter as shown in Fig. 65A, and the back surface is a rotationally-asymmetrical 15 aspherical surface whose curvature is distributed among 13.02 to 19.05 Diopter as shown in Fig. 65B. The center thickness of the lens of the eighth embodiment is 1.10mm.

Fig. 66 is a graph showing variation of C2 (h, 0+180)-C2 (h, O) that is left side of the condition (1) with respect to 20 variation of the angle 9. The values of the left side of the condition (1) rise to maximums at = 90 and are reduced to minimums at 0 = 270 for the distances h = 10, 15 and 20 mm.

Fig. 66 shows that the values indicated in the graph are larger than zero in the range of 30 150 and 10 h 20.

25 Namely, the aspherical spectacle lens of the eighth embodiment

satisfies the condition (1).

Figs. 67A and 67B are graphs showing variations of curvatures C:(h, O) and C (h,2 O) of the front and back surfaces, respectively, with respect to variation of the 5 distance h from the framing reference point. Since the front surface is a rotationally-symmetrical aspherical surface, the curvature varies according to variation of the distance h while the variation of the angle does not change the curvature. In the graph of Fig. 67A, the curves of all of the 10 angles are overlapped. Since the back surface is rotationally-

asymmetrical, the curvature C2(h, O) varies according to variations of the distance h and the angle O. In the graph of Fig. 67B, the curve of 0 = 90 , the curve of 0 = 270 , the overlapped curves of 0 = 45 and 135 , the overlapped curves 15 of 6 - 225 and 315 , the overlapped curves of = 0 and 180 are arranged in increasing order of curvature.

Figs. 68A and 68B are graphs showing variations of curvatures C (h, O) and C2(h, O) of the front and back surfaces, respectively, with respect to variation of the angle 20 0. Since the front surface is a rotationallysymmetrical aspherical surface, the curvatures C:(h, O) are different in response to the distance h and do not vary according to variation of the angle 0, the curvatures are shown as independent straight lines. The curvature of the back surface 25 becomes large at 0 = 0 and 180 and becomes small at = 90

- 47 -

and 270 due to the added cylindrical power, in general.

However, the curvature at the side of the prism base (O = 270 ) is larger than that at the side of the apex (0 = 90 ) in order to correct the aberration caused by adding the base-down 5 prismatic power.

Further, Figs. 69A and 69B are graphs showing variations of C (h, 0+180)C1(h, O) that is the left side of the condition (3) and C2(h, O+180)-C2(h, O) that is the left side of the condition (2), respectively, with respect to variation 10 of the angle 0. Since the front surface is rotationaly-

symmetrical, the value of the left side of the condition (3) remains constant. The value of the left side of the condition (2) varies according to variations of the angle 0 and the distance h. Fig. 69B shows that the values indicated in the 15 graph are larger than zero in the range of 30 3 150 and 10 < h 20. Namely, the aspherical spectacle lens of the eighth embodiment satisfies the condition (2).

Figs. 70A and 70B are three-dimension graphs showing transmitting optical performances of the aspherical spectacle 20 lens of the eighth embodiment; Fig. 70A shows an average refractive power error and Fig. 70B shows astigmatism.

Fourth Comparative Example In the same manner as the seventh and eighth embodiments, 25 the aspherical spectacle lens of the fourth comparative

- 48 example satisfies the specification of TABLE 4, the front

surface is a rotationally-symmetrical aspherical surface whose curvature at the framing reference point is 1.01 Diopter as shown in Fig. 71A, and the back surface is a toric surface 5 whose curvature is distributed among 13.04 to 19.05 Diopter as shown in Fig. 71B. The center thickness of the lens of the fourth comparative example is 1.10mm.

Fig. 72 is a graph showing variation of C2l(h, O+180)-C2 l(h, O) that is left side of the condition (1) with respect to 10 variation of the angle 0. Since the front surface is rotationally-symmetrical and the back surface is symmetric with respect to the framing reference point, the value of the left side of the condition (1) remains constant. Namely, the aspherical spectacle lens of the fourth comparative example 15 does not satisfy the condition (1).

Figs. 73A and 73B are graphs showing variations of curvatures Cl(h, 9) and C2(h, O) of the front and back surfaces, respectively, with respect to variation of the distance h from the framing reference point. Since the front 20 surface is a rotationally-symmetrical aspherical surface, the curvature varies according to variation of the distance h while the variation of the angle does not change the curvature. In the graph of Fig. 73A, the curves of all of the angles are overlapped. Since the back surface is toric, the 25 curvature varies according to variation of the angle O.

- 49 However, the curvature of the toric surface does not vary according to variation of the distance h. Therefore, in the graph of Fig. 73B, the overlapped straight lines of = 90 and 270 , the overlapped straight lines of = 45 , 135 , 225 5 and 315 , the overlapped straight lines of = 0 and 180 are arranged in increasing order of the curvature.

Figs. 74A and 74B are graphs showing variations of curvatures C (h, O) and C2(h, 0) of the front and back surfaces, respectively, with respect to variation of the angle 10 O. Since the front surface is a rotationallysymmetrical aspherical surface, the curvatures C (h, O) are different in response to the distance h and do not vary according to variation of the angle 8, the curvatures are shown as independent straight lines. The curvature C2(h, 6) of the 15 toric back surface is reduced to a minimum at = 90 and 270 and rises to a minimum at 0 = 0 and 180 as shown in Fig. 74B. Further, Figs. 75A and 75B are graphs showing variations of C1(h, 0+180)-Cl(h, O) that is the left side of the 20 condition (3) and C2(h, 0+180)-C2(h, O) that is the left side of the condition (2), respectively, with respect to variation of the angle 0. Since the front surface is a rotationally-

symmetrical aspherical surface, the value of the left side of the condition (3) remains constant. Further, since the back 25 surface is toric, the value of the left side of the condition

(2) remains constant. Namely, the spectacle lens of the fourth comparative example does not satisfy the conditions (2) and (3).

Figs. 76A and 76B are three-dimension graphs showing 5 transmitting optical performances of the aspherical spectacle lens of the fourth comparative example) Fig. 76A shows an average refractive power error and Fig. 76B shows astigmatism.

As compared with the graphs of the seventh and eighth embodiments (Figs. 64A, 64B, 70A and 70B) designed for the 10 same specification, a number of contour lines in either graph

of the fourth comparative example is larger than that of the embodiments, which shows that the optical performance of the embodiments is better than the comparative example.

15 Ninth Embodiment The spectacle lenses of the ninth and tenth embodiments and the fifth comparative example are designed for satisfying the specification shown in TABLE 5. Each of these lenses has

a prismatic power to correct hereophoria while they do not 20 have a cylindrical power to correct astigmatism.

- 51 TABLE 5

SPH 4.00 Diopter CYL 0.00 Diopter AX 5 PRS 3.00

BASE 270 Base Down The aspherical spectacle lens of the ninth embodiment satisfies the specification of TABLE 5, the front surface is

10 a spherical surface that has a uniform curvature 6.96 Diopter as shown in Fig. 77A, and the back surface is a rotationally-

asymmetrical aspherical surface whose curvature at the framing reference point is distributed among 1.05 to 1.06 Diopter as shown in Fig. 77B. The center thickness of the lens of the 15 fifth embodiment is 5.29mm.

Fig. 78 is a graph showing variation of C21(h, O+180)-C2 :(h, O) that is left side of the condition (1) with respect to variation of the angle 0. In order to correct the aberration caused by adding the prismatic power, the values of the left 20 side of the condition (1) rise to maximums at = 90 and are reduced to minimums at = 270 for all of the distances h = 10, 15, 20 and 25 mm. The amplitude of the variation increases as the distance h becomes larger. Fig. 78 shows that the values indicated in the graph are larger than zero 25 in the range of 30 < 3 150 for all of the distances h = 10, 15, 20 and 25 mm. Namely, the aspherical spectacle lens of the ninth embodiment satisfies the condition (1).

Figs. 79A and 79B are graphs showing variations of curvatures C (h, O) and C2(h, O) of the front and back surfaces, respectively, with respect to variation of the distance h from the framing reference point. Since the front 5 surface is spherical, the curvature C (h, S) does not vary according to variations of the distance h and the angle a, the graph of Fig. 79A shows the straight lines overlapped to each other. Since the back surface is rotationally-asymmetrical, the curvature C2(h, 0) varies according to variations of the 10 distance h and the angle 0. In the graph of Fig. 79B, the curve of = 90 , the overlapped curves of = 45 and 135 , the overlapped curves of = 0 and 180 , the overlapped curves of 0 = 225 and 315 and the curve of = 270 are arranged in increasing order of curvature.

15 Figs. 80A and 80B are graphs showing variations of curvatures C (h, O) and C2(h, O) of the front and back surfaces, respectively, with respect to variation of the angle O. Since the front surface is spherical, the curvature C (h, 9) does not vary according to variations of the distance h and 20 the angle 6, the graph of Fig. 80A shows the straight lines overlapped to each other. In order to correct the aberration caused by adding the base-down prismatic power, the curvatures C2(h, 0) of the back surface are reduced to minimums at 0 = 90 and rise to maximums at 9 = 270 for all of the distances 25 h = 10, 15, 20 and 25 mm as shown in Fig. BOB. The longer the

- 53 distance h is, the larger the curvature C2(h, O) is.

Further, Figs. 81A and 81B are graphs showing variations of C (h, O+180)C1(h, O) that is the left side of the condition (3) and C2(h, O+180)-C2(h, O) that is the left side 5 of the condition (2), respectively, with respect to variation of the angle O. Since the front surface is spherical, the value of the left side of the condition (3) remains constant.

The value of the left side of the condition (2) varies according to variations of the angle and the distance h. 10 Fig. 81B shows that the values indicated in the graph are larger than zero in the range of 30 150 for all of the distances h = 10, 15, 20 and 25 mm. Namely, the aspherical spectacle lens of the ninth embodiment satisfies the condition (2). 15 Figs. 82A and 82B are three-dimension graphs showing transmitting optical performances of the aspherical spectacle lens of the ninth embodiment; Fig. 82A shows an average refractive power error and Fig. 82B shows astigmatism.

20 Tenth Embodiment In the same manner as the ninth embodiment, the aspherical spectacle lens of the tenth embodiment satisfies the specification of TABLE 5, the front surface is a

rotationally-asymmetrical aspherical surface whose curvature 25 at the framing reference point is 7.16 Diopter as shown in

- 54 Fig. 83A, and the back surface is a rotationally-symmetrical aspherical surface whose curvature at the framing reference point is 1.26 Diopter as shown in Fig. 83B. The center thickness of the lens of the second embodiment is 5.30mm.

5 Fig. 84 is a graph showing variation of C2 (h, 0+180)-C2 :(h, O) that is left side of the condition (1) with respect to variation of the angle 9. In order to correct the aberration caused by adding the prismatic power, the values of the left side of the condition (1) rise to maximums at = 90 and are 10 reduced to minimums at a = 270 for all of the distances h = 10, 15, 20 and 25 mm. The amplitude of the variation increases as the distance h becomes larger. Fig. 84 shows that the values indicated in the graph are larger than zero in the range of 30 < < 150 for all of the distances h = 10, 15 15, 20 and 25 mm. Namely, the aspherical spectacle lens of the tenth embodiment satisfies the condition (1).

Figs. 85A and 85B are graphs showing variations of curvatures C1(h, 9) and C2(h, 0) of the front and back surfaces, respectively, with respect to variation of the 20 distance h from the framing reference point. Since the front surface is rotationally-asymmetrical, the curvature C (h, 9) varies according to variations of the distance h and the angle O. In the graph of Fig. 85A, the curve of = 270 , the overlapped curves of = 225 and 315 , the overlapped curves 25 of = 0 and 180 , the overlapped curves of = 45 and 135

- 55 and the curve of 0 = 90 are arranged in increasing order of curvature. Since the back surface is a rotationally symmetrical aspherical surface, the curvature varies according to variation of the distance h while the variation of the 5 angle 0 does not change the curvature. In the graph of Fig. 85B, the curves of all of the angles are overlapped.

Figs. 86A and 86B are graphs showing variations of curvatures C:(h, 9) and C2(h, 0) of the front and back surfaces, respectively, with respect to variation of the angle 10 9. In order to correct the aberration caused by adding the base-down prismatic power, the curvatures C (h, 3) of the front surface rise to maximums at 0 = 90 and are reduced to minimums at 0 = 270 for all of the distances h = 15, 20 and 25 mm as shown in Fig. 86A. Since the back surface is a IS rotationally-symmetrical aspherical surface, the curvatures C2(h, 3) are different in response to the distance h and do not vary according to variation of the angle 0, the curvatures are shown as independent straight lines in Fig. 86B.

Further, Figs. 87A and 87B are graphs showing variations 20 of Cl(h, O+ 180)-C (h, O) that is the left side of the condition (3) and C2(h, 0+180)C2(h, O) that is the left side of the condition (2), respectively, with respect to variation of the angle 0. The values of the left side of the condition (3) vary according to variations of the angle and the 25 distance h. Fig. 87A shows that the values indicated in the

- 56 graph are smaller than zero in the range of 30 s 150 and 10 h 20mm. Namely, the aspherical spectacle lens of the tenth embodiment satisfies the condition (3). Since the back surface is rotationally-symmetrical, the values of the left 5 side of the condition (2) remain constant.

Figs. 88A and 88B are three-dimension graphs showing transmitting optical performances of the aspherical spectacle lens of the tenth embodiment) Fig. 88A shows an average refractive power error and Fig. 88B shows astigmatism.

Fifth Comparative Example In the same manner as the ninth and tenth embodiments, the aspherical spectacle lens of the fifth comparative example satisfies the specification of TABLE 5, the front surface is

* a rotationally-symmetrical aspherical surface whose curvature at the framing reference point is 7.17 Diopter as shown in Fig. 89A, and the back surface is a spherical surface that has a uniform curvature 1.26 Diopter as shown in Fig. 89B. The center thickness of the lens of the first comparative example 20 is 5.29mm.

Fig. 90 is a graph showing variation of C21(h, O+180)-C2 l(h, 9) that is left side of the condition (1) with respect to variation of the angle 3. Since the front and back surfaces are rotationally-symmetrical, the value of the left side of 25 the condition (1) remains constant. Namely, the aspherical

- 57 spectacle lens of the fifth comparative example does not satisfy the condition (1).

Figs. 91A and 91B are graphs showing variations of curvatures C1(h, 9) and C2(h, 9) of the front and back 5 surfaces, respectively, with respect to variation of the distance h from the framing reference point. Since the front surface is a rotationally-symmetrical aspherical surface, the curvature varies according to variation of the distance h while the variation of the angle a does not change the 10 curvature. In the graph of Fig. 91A, the curves of all of the angles are overlapped. Since the back surface is spherical, the curvature does not vary according to variations of the distance h and the angle 6, the graph of Fig. 91B shows the straight lines overlapped to each other.

15 Figs. 92A and 92B are graphs showing variations of curvatures C:(h, O) and C2(h, O) of the front and back surfaces, respectively, with respect to variation of the angle 0. Since the front surface is a rotationallysymmetrical aspherical surface, the curvatures C (h, O) are different in 20 response to the distance h and do not vary according to variation of the angle 8, the curvatures are shown as independent straight lines in Fig. 92A. Since the back surface is spherical, the curvature C2(h, O) does not vary according to variations of the distance h and the angle 6, the 25 graph of Fig. 92B shows the straight lines overlapped to each

- 58 other. Further, Figs. 93A and 93B are graphs showing variations of C1(h, O+180)-C (h, p) that is the left side of the condition (3) and C2(h, O+180)-C2(h, O) that is the left side 5 of the condition (2), respectively, with respect to variation of the angle 9. Since the front surface is a rotationally-

symmetrical aspherical surface, the value of the left side of the condition (3) remains constant. Further, since the back surface is spherical, the value of the left side of the 10 condition (2) remains constant. Namely, the spectacle lens of the fifth comparative example does not satisfy the conditions (2) and (3).

Figs. 94A and 94B are three-dimension graphs showing transmitting optical performances of the aspherical spectacle 15 lens of the fifth comparative example) Fig. 94A shows an average refractive power error and Fig. 94B shows astigmatism.

As compared with the graphs of the ninth and tenth embodiments (Figs. 82A, 82B, 88A and 88B) designed for the same specification, a number of contour lines in either graph of

20 the fifth comparative example is larger than that of the embodiments, which shows that the optical performance of the embodiments is better than the comparative example.

Eleventh Embodiment 25 The spectacle lenses of the eleventh and twelfth

- 59 -

embodiments and the sixth comparative example are designed for satisfying the specification shown in TABLE 6. Each of these

lenses has a prismatic power to correct hereophoria and a cylindrical power to correct astigmatism.

TABLE 6

SPH 4.00 Diopter CYL -4.00 Diopter AX 45o 10 PRS 3.00

BASE 270 Base Down The aspherical spectacle lens of the eleventh embodiment satisfies the specification of TABLE 6, the front surface is

15 a spherical surface that has a uniform curvature 6.96 Diopter as shown in Fig. 95A, and the back surface is a rotationally-

asymmetrical aspherical surface whose curvature at the framing reference point is distributed among 1.06 to 7.07 Diopter as shown in Fig. 95B. The center thickness of the lens of the 20 eleventh embodiment is 5.29mm. The back surface contains a first rotationally-asymmetrical component to correct the aberration caused by adding a prismatic power and a second rotationally-asymmetrical component to add a cylindrical power. Therefore, any rotationally-asymmetrical component is 25 not required for the front surface, which allows the front surface to be formed as a spherical surface.

Fig. 96 is a graph showing variation of Cash, O+180)-C2

:(h, O) that is left side of the condition (1) with respect to variation of the angle O. The values of the left side of the condition (1) rise to maximums at = 110 and are reduced to minimums at = 290 for the distances h = 10, 15, 20 and 5 25mm. The amplitude of the variation increases as the distance h becomes larger. Fig. 96 shows that the values indicated in the graph are larger than zero in the range of 30 150 for all of the distances h = 10, 15, 20 and 25 mm. Namely, the aspherical spectacle lens of the eleventh 10 embodiment satisfies the condition (1).

Figs. 97A and 97B are graphs showing variations of curvatures C (h, O) and C2(h, O) of the front and back surfaces, respectively, with respect to variation of the distance h from the framing reference point. Since the front 15 surface is spherical, the curvature C (h, O) does not vary according to variations of the distance h and the angle 0, the graph of Fig. 97A shows the straight lines overlapped to each other. Since the back surface is rotationally-asymmetrical, the curvature C2(h, 6) varies according to variations of the 20 distance h and the angle O. In the graph of Fig. 97B, the curve of 3 = 45 , the curve of 9 = 225 , the curve of = 90 , the curve of = 0 , the curve of = 270 , the curve of 9 = 315 and the curve of = 315 are arranged in increasing order of curvature.

25 Figs. 98A and 98B are graphs showing variations of

curvatures C1(h, O) and C]h, O) of the front and back surfaces, respectively, with respect to variation of the angle 9. Since the front surface is spherical, the curvature Cl(h, O) does not vary according to variations of the distance h and 5 the angle 0, the graph of Fig. 98A shows the straight lines overlapped to each other. The curvature of the back surface becomes large at 9 = 135 and 315 and becomes small at a = 45 and 225 due to the added cylindrical power, in general.

However, the curvature at the side of the prism base (O = 10 270 ) is larger than that at the side of the apex (O = 90 ) in order to correct the aberration caused by adding the base-down prismatic power.

Further, Figs. 99A and 99B are graphs showing variations of C1(h, O+180)C (h, O) that is the left side of the 15 condition (3) and C2(h, O+180)C2(h, O) that is the left side of the condition (2), respectively, with respect to variation of the angle O. Since the front surface is spherical, the value of the left side of the condition (3) remains constant.

The value of the left side of the condition (2) varies 20 according to variations of the angle and the distance h. Fig. 99B shows that the values indicated in the graph are larger than zero in the range of 30 0 150 for all of the distances h = 10, 15, 20 and 25 mm. Namely, the aspherical spectacle lens of the eleventh embodiment satisfies the 25 condition (2).

- 62 Figs. lOOA and lOOB are three-dimension graphs showing transmitting optical performances of the aspherical spectacle lens of the eleventh embodiment) Fig. lOOA shows an average refractive power error and Fig. lOOB shows astigmatism.

Twelfth Embodiment In the same manner as the eleventh embodiment, the aspherical spectacle lens of the twelfth embodiment satisfies the specification of TABLE 6, the front surface is a

10 rotationally-asymmetrical aspherical surface whose curvature at the framing reference point is distributed among 4.23 to 7.16 Diopter as shown in Fig. lOlA, and the back surface is an atoric surface whose curvature at the framing reference point is distributed among 1.26 to 4. 27Diopter as shown in 15 Fig. lOlB. The center thickness of the lens of the second embodiment is 5.30mm. The rotationally-asymmetrical front surface contains the first rotationally-asymmetrical component to correct the aberration caused by adding the prismatic power, and the atoric back surface contains the second 20 rotationally-asymmetrical component to add the cylindrical power. Fig. 102 is a graph showing variation of C2l(h, O+ 180)-C2 Ah, O) that is left side of the condition (1) with respect to variation of the angle O. The values of the left side of the 25 condition (1) rise to maximums at = 105 and are reduced to

- 63 minimums at = 285 for all of the distances h = 10, 15, 20 and 25 mm. Fig. 102 shows that the values indicated in the graph are larger than zero in the range of 30 150 for all of the distances h = 10, 15, 20 and 25 mm. Namely, the 5 aspherical spectacle lens of the twelfth embodiment satisfies the condition (1).

Figs. 103A and 103B are graphs showing variations of curvatures Cl(h, O) and C2(h, O) of the front and back surfaces, respectively, with respect to variation of the 10 distance h from the framing reference point. Since the front and back surfaces are rotationally-asymmetrical, the curvatures C (h, O) and C2(h, 0) vary according to variations of the distance h and the angle O. In the graph of Fig. 103A, the curve of 0 = 315 , the curve of = 135 , the curve of 15 = 270 , the overlapped curves of = 0 and 180 , the curve of = 90 , the curve of = 225 and the curve of 0 = 45 are arranged in increasing order of curvature within the range of 10 < h 20. In the graph of Fig. 103B, the overlapped curves of = 45 and 225 , theoverlapped curves of = 0 , 90 , 180 20 and 270 , the overlapped curves of Q = 135 and 315 are arranged in increasing order of curvature.

Figs. 104A and 104B are graphs showing variations of curvatures C (h, O) and C2(h, 0) of the front and back surfaces, respectively, with respect to variation of the angle 25 O. In order to correct the aberration caused by adding the

- 64 base-down prismatic power, the curvature Cl(h, O) of the front surface at the side of the prism base (O = 270 ) is larger than that at the side of the apex (0 = 90 ). The curvature of the atoric back surface becomes large at = 135 and 315 and 5 becomes small at a = 45 and 225 due to the added cylindrical power. Further, Figs. 105A and 105B are graphs showing variations of Cl(h, 0+180)-Cl(h, O) that is the left side of the condition (3) and C2(h, 0+180)-C2(h, 3) that is the left 10 side of the condition (2), respectively, with respect to variation of the angle 0. The values of the left side of the condition (3) vary according to variations of the angle and the distance h. Fig. 105A shows that the values indicated in the graph are smaller than zero in the range of 30 s 0 s 150 15 for all of the distances h = 10, 15, 20 and 25mm. Namely, the aspherical spectacle lens of the twelfth embodiment satisfies the condition (3). Since the back surface is an atoric surface whose variation of curvature is symmetric with respect to the framing reference point, the values of the left side 20 of the condition (2) remain constant.

Figs. 106A and 106B are three-dimension graphs showing transmitting optical performances of the aspherical spectacle lens of the twelfth embodiment; Fig. 106A shows an average refractive power error and Fig. 106B shows astigmatism.

- 65 Sixth Comparative Example In the same manner as the eleventh and twelfth embodiments, the aspherical spectacle lens of the sixth comparative example satisfies the specification of TABLE 6,

5 the front surface is a rotationally-symmetrical aspherical surface whose curvature at the framing reference point is 7.17 Diopter as shown in Fig. 107A, and the back surface is a toric surface whose curvature is distributed among 1.26 to 7.27 Diopter as shown in Fig. 71B. The center thickness of the 10 lens of the fourth comparative example is 5.29mm.

Fig. 108 is a graph showing variation of C2l(h, O+180)-C2 Ah, O) that is left side of the condition (1) with respect to variation of the angle O. Since the front surface is rotationally-symmetrical and the back surface is symmetric 15 with respect to the framing reference point, the value of the left side of the condition (1) remains constant. Namely, the aspherical spectacle lens of the sixth comparative example does not satisfy the condition (1).

Figs. lO9A and lO9B are graphs showing variations of 20 curvatures C (h, 9) and C2(h, 9) of the front and back surfaces, respectively, with respect to variation of the distance h from the framing reference point. Since the front surface is a rotationally-symmetrical aspherical surface, the curvature varies according to variation of the distance h 25 while the variation of the angle does not change the

- 66 curvature. In the graph of Fig. lO9A, the curves of all of the angles are overlapped. Since the back surface is toric, the curvature varies according to variation of the angle 0.

However, the curvature of the toric surface does not vary 5 according to variation of the distance h. Therefore, in the graph of Fig. 109B, the overlapped straight lines of = 45 and 225 , the overlapped straight lines of = 0 , 90 , 180 and 270 , the overlapped straight lines of 3 = 135 and 315 are arranged in increasing order of the curvature.

10 Figs. llOA and llOB are graphs showing variations of curvatures C (h, O) and C2(h, O) of the front and back surfaces, respectively, with respect to variation of the angle 0. Since the front surface is a rotationally-symmetrical aspherical surface, the curvatures C (h, O) are different in 15 response to the distance h and do not vary according to variation of the angle 8, the curvatures are shown as independent straight lines. The curvature C2(h, 9) of the toric back surface is reduced to a minimum at = 45 and 225 and rises to a maximum at = 135 and 315 as shown in Fig. 20 llOB.

Further, Figs. lllA and lllB are graphs showing variations of C1(h, 0+180) -C (h, O) that is the left side of the condition (3) and C2(h, 0+180)C2(h, 0) that is the left side of the condition (2), respectively, with respect to 25 variation of the angle O. Since the front surface is a

- 67 -

rotationally-symmetrical aspherical surface, the value of the left side of the condition (3) remains constant Further, since the back surface is toric, the value of the left side of the condition (2) remains constant. Namely, the spectacle 5 lens of the sixth comparative example does not satisfy the conditions (2) and (3).

Figs. 112A and 112B are three-dimension graphs showing transmitting optical performances of the aspherical spectacle lens of the sixth comparative example; Fig. 112A shows an 10 average refractive power error and Fig. 112B shows astigmatism. As compared with the graphs of the eleventh and twelfth embodiments (Figs. lOOA, lOOB, 106A and 106B) designed for the same specification, a number of contour lines in

either graph of the sixth comparative example is larger than 15 that of the embodiments, which shows that the optical performance of the embodiments is better than the comparative example.

Claims (8)

À 68 Claims:

1. An aspherical spectacle lens having a prismatic power for 5 correcting hereophoria of an eye, the lens comprising: a front surface; and a back surface, wherein at least one of said front and back surfaces is a rotationally-asymmetrical aspherical surface that has a 10 rotationallyasymmetrical component for correcting the aberrations caused by adding said prismatic power.

2. An aspherical spectacle lens according to claim 1, wherein said back surface is said rotationally-asymmetrical 15 aspherical surface, and assuming that a framing reference point is coincident with a pupil position of a user when the spectacle lens is installed on a frame, a curvature of an intersection line of a plane containing the normal to said rotationally-asymmetrical surface at said framing reference 20 point and said rotationally-asymmetrical surface at the prism base side is larger than that at the apex side.

3. An aspherical spectacle lens according to claim 1, wherein said front surface is said rotationally-asymmetrical 25 aspherical surface, and assuming that a framing reference

- 69 point is coincident with a pupil position of a user when the spectacle lens is installed on a frame, curvature of an intersection line of a plane containing the normal to said rotationally-asymmetrical surface at said framing reference 5 point and said rotationally- asymmetrical surface at the prism base side is smaller than that at the apex side.

4. An aspherical spectacle lens according to claim 1, wherein the condition (1) is satisfied within the ranges of 10 10 h 20 and 30 150; C2l(h, O+l8o)-c2- (h' o) > 0... (1 where C21(h, O) = C2(h, 0) - C1(h, 0); C1(h, 0) is curvature of an intersection line of a plane, 15 which contains a z1-axis and forms angle (degree) with respect to an x1-axis, and said front surface at a point whose distance from a zl-axis is h (mm); C2(h, 9) is curvature of an intersection line of a plane, which contains a z2-axis and forms angle (degree) with 20 respect to an x2-axis, and said back surface at a point whose distance from a z2-axis is h (mm); z1- axis is a normal to said front surface at a framing reference point that is coincident with a pupil position of a user when the spectacle lens is installed on a frame; 25 y,-axis is direction from the base to the apex in a plane

- 70 perpendicular to the z1-axis; x1-axis is perpendicular to both of the Y1- and z1-axes in a left-hand coordinate system) z2-axis is a normal to said back surface at said framing 5 reference point) y2-axis is direction from the base to the apex in a plane perpendicular to the z2- axisi and x2-axis is perpendicular to both of the Y2- and z2-axes in a left-hand coordinate system.

5. An aspherical spectacle lens according to claim 1 or 2 wherein said back surface is said rotationally-asymmetrical surface and the condition (2) is satisfied within the ranges of 10 h 20 and 30 < < 150i 15 C2(h, O+ 180)-C2(h, O) > 0 (2) where C2(h, O) is curvature of an intersection line of a plane, which contains a z2-axis and forms angle (degree) with respect to an x2-axis, and said back surface at a point whose 20 distance from a z2-axis is h (mm)i z2-axis is a normal to said back surface at a framing reference point that is coincident with a pupil position of a user when the spectacle lens is installed on a frame; y2-axis is direction from the base to the apex in a plane 25 perpendicular to the z2- axis; and

- 71 x2-axis is perpendicular to both of the Y2- and z2-axes in a lefthand coordinate system.

6. An aspherical spectacle lens according to claim 1 or 3 5 wherein said front surface is said rotationally-asymmetrical surface and the condition (3) is satisfied within the ranges of 10 h 20 and 30 150i C:(h, O+180)-C (h, 0) < 0...(3) where 10 C:(h, O) is curvature of an intersection line of a plane, which contains a zi-axis and forms angle (degree) with respect to an x-axis, and said front surface at a point whose distance from a z1-axis is h (mm); z -axis is a normal to said front surface at a framing 15 reference point that is coincident with a pupil position of a user when the spectacle lens is installed on a frame; y:-axis is direction from the base to the apex in a plane perpendicular to the z1- axis; and x -axis is perpendicular to both of the ye- and z -axes 20 in a left-hand coordinate system.

7. An aspherical spectacle lens according to claim 1, wherein said front surface is spherical and said back surface is rotationally-asymmetrical.

- 72

8. An aspherical spectacle lens substantially as hereinbefore described with reference to the attached Figures.